1
ALICE rf project meeting
Kai Hock, Cockcroft / Liverpool
19 May 2008
2
Status
•
Aug

Dec 07: 4GLS beam loading (Hywel, Yuri)
–
Worked through Wiedemann’s chapter, Perry Wilson’s report on rf system
–
Reproduced simulation on 4GLS beam loading (Sakanaka ERL07)
–
Report on beam loading
–
basics, 4GLS
•
Feb 08: ALICE rf control
–
new phase
•
Mar 08: ALICE
–
intro to rf system (Andy)
•
Apr 08:
–
Contacted, received paper, suggestions from Tom Powers
–
Looking up references: rf feedback, energy recovery theory, …
–
Started learning rf control hardware, set up by Andy
–
Idea: connect cavity / stretched wire to simulate beam loading
•
May 08
–
Simulation on klystron power
–
with energy recovery ?
–
Set up stretched wire experiments ?
3
RF system theory
•
Feedback control
experiments
–
Stefan Simrock’s LLRF lectures
–
Papers on ELBE rf system
•
Beam loading
–
Wiedemann’s textbook, Wilson’s SLAC report (beam loading)
–
Sakanaka’s ERL07 paper (4GLS simulation)
•
Energy recovery linac
–
Thomas Schilcher’s PhD thesis (microphonics, Lorentz detuning)
–
Lia Merminga’s 2001 USPAS lectures (beam loading in ERL)
–
Tom Power’s paper
4
Deciphering Tom’s paper
•
Why / how does energy recovery happen?
•
What are r/Q,
Q
L
, Q
0
,
,
f
S
,
B
, …
?
•
How does the klystron power equation come about?
•
What are microphonics, Lorentz detuning, ponderomotive
effects, vector sum, … ?
•
Why are we interested in detuning? What are mechanical
tuners?
•
Why is detuning measured by the Klystron

cavity phase
difference?
•
When Q
L
is optimized, what exactly is minimised or
maximised? The klystron power?
•
Why is incomplete energy recovery needed? How does
this compress the energy spread?
•
What are page 2, page 3, page 4 and page 5 about?
Questions from a complete beginner
5
Finding Answers
Why Energy Recovery
“ … the beam

induced voltage in a cavity is the same
whether or not a generator voltage component is present.”
(Wilson 1991,
sect. 6.1 The Fundamental Theorem of Beam Loading )
The beam induced voltage is always negative.
Therefore, if a bunch enters at the opposite phase
of the cavity field, it will increase the amplitude of
the field.
This gives energy to the cavity.
(Sakanaka ERL07)
6
Finding Answers
Shunt Impedance
(Wiedemann 2003)
A full calculation from Maxwell’s equations for pillbox cavity:
7
Finding Answers
Many equations come from this !
(Wiedemann 2003)
8
Finding Answers
r/Q,
Q
L
, Q
0
,
,
B
, …
(Wiedemann 2003)
This
models
the behaviour of
the cavity voltages.
Mostly using
equations from
simple harmonic
oscillator.
9
Finding Answers
How the beam affects the cavity voltage
All voltages defined along the axis of cavity (beam path):
generator (klystron) voltage V
g
beam induced voltage V
b
and resultant cavity voltage V
c
Assuming all sinusoidal, they can be related by a phasor diagram.
(Wilson 1991)
10
Finding Answers
The klystron power equation
2 2
2
0 0
(1 )
1 cos tan sin
4
c L L
g b b
L c c
V I R I R
P
R V V
r/Q,
Q
L
, Q
0
,
, … are measured
by fitting to the equivalent circuit model
The klystron power can be calculated
from these parameters using the model.
Merminga (2001) explains how to get this:
Steps are easy once we have worked from
Wiedemann and Wilson.
The main equation
in Tom’s paper
11
Finding Answers
Energy recovery calculations
ERL Injector and Linac:
f
m
=25 Hz, Q
0
=1x10
10
, f
0
=1300 MHz, I
0
=100 mA, V
c
=20 MV/m, L=1.04 m,
R
a
/Q
0
=1036
ohms per cavity
ERL linac: Resultant beam current, I
tot
= 0 mA (energy recovery)
and
opt
=385
Q
L
=2.6x10
7
P
g
= 4 kW per cavity.
ERL Injector: I
0
=100 mA and
opt
= 5x10
4
!
Q
L
= 2x10
5
P
g
= 2.08 MW
per cavity!
Note: I
0
V
a
= 2.08 MW
optimization is entirely dominated by beam loading.
Nice examples from Merminga (2001)
12
Finding Answers
Microphonics, Lorentz Force, Vector Sum
(Schilcher 1998)
Revelation !
13
Finding Answers
What exactly is being optimized?
(Liepe PAC05)
The klystron power, of course !
14
Finding Answers
Ponderomotive force
15
Finding Answers
Page 2 of Tom’s paper
One bunch at a time?
10
o
165
o
1
st
pass
2
nd
pass
I
B
?
Shall try to do this next
16
Experiments
•
References on Feedback control
–
Stefan Simrock’s LLRF lectures
–
Papers on ELBE rf system
•
Andy’s Rossendorf control unit
–
Connect control system to standalone cavity
–
Stretched wire measurements with short pulses
•
Ideas for experiments
–
For learning about rf control
–
For modelling of beam loading / energy recovery
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